Apollonius <Pergaeus>; Lawson, John, The two books of Apollonius Pergaeus, concerning tangencies, as they have been restored by Franciscus Vieta and Marinus Ghetaldus : with a supplement to which is now added, a second supplement, being Mons. Fermat's Treatise on spherical tangencies

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[31.] PROBLEM II.
[32.] PROBLEM III.
[33.] PROBLEM IV.
[34.] PROBLEM V.
[35.] PROBLEM VI.
[36.] General Solution.
[37.] A SECOND SUPPLEMENT, BEING Monſ. DE FERMAT’S Treatiſe on Spherical Tangencies. PROBLEM I.
[38.] PROBLEM II.
[39.] PROBLEM III.
[40.] PROBLEM IV.
[41.] PROBLEM V.
[42.] PROBLEM VI.
[43.] PROBLEM VII.
[44.] LEMMA I.
[45.] LEMMA II.
[46.] LEMMA III.
[47.] LEMMA IV.
[48.] LEMMA V.
[49.] PROBLEM VIII.
[50.] PROBLEM IX.
[51.] PROBLEM X.
[52.] PROBLEM XI.
[53.] PROBLEM XII.
[54.] PROBLEM XIII.
[55.] PROBLEM XIV.
[56.] PROBLEM XV.
[57.] Synopſis of the PROBLEMS.
[58.] THE TWO BOOKS OF APOLLONIUS PERGÆUS, CONCERNING DETERMINATE SECTION, As they have been Reſtored by WILLEBRORDUS SNELLIUS. By JOHN LAWSON, B. D. Rector of Swanſcombe, Kent. TO WHICH ARE ADDED, THE SAME TWO BOOKS, BY WILLIAM WALES, BEING AN ENTIRE NEW WORK. LONDON: Printed by G. BIGG, Succeſſor to D. LEACH. And ſold by B. White, in Fleet-Street; L. Davis, in Holborne; J. Nourse, in the Strand; and T. Payne, near the Mews-Gate. MDCC LXXII.
[59.] ADVERTISEMENT.
[60.] EXTRACT from PAPPUS's Preface to his Seventh Book in Dr. HALLEY's Tranſlation. DE SECTIONE DETERMINATA II.
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31(19)
A SECOND
SUPPLEMENT,
BEING
Monſ. DE FERMAT’S Treatiſe on
Spherical Tangencies.
PROBLEM I.
HAVING four points N, O, M, F, given, to deſcribe a ſphere which
ſhall paſs through them all.
Taking any three of them N, O, M, ad libitum, they will form a triangle,
about which a circle ANOM may be circumſcribed, which will be given in
magnitude and poſition.
That this circle is in the ſurface of the ſphere
ſought appears from hence;
becauſe if a ſphere be cut by any plane, the
ſection will be a circle;
but only one circle can be drawn to paſs through the
three given points N, O, M;
therefore this circle muſt be in the ſurface of
the ſphere.
Let the center of this circle be C, from whence let CB be
erected perpendicular to it’s plane;
it is evident that the center of the ſphere
ſought will be in this line CB.
From the fourth given point F let FB be
drawn perpendicular to CB, which FB will be alſo given in magnitude and
poſition.
Through C draw ACD parallel to FB, and this line will be

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